hole vs mouth hole

hole and mouth hole both are nouns.

Word	Noun	Adjective	Verb	Adverb
hole	Yes	No	Yes	No
mouth hole	Yes	No	No	No

As nouns, mouth hole is a hyponym of hole; that is, mouth hole is a word with a more specific, narrower meaning than hole:

hole (noun)	mouth hole (noun)
an opening deliberately made in or through something	a hole (as in a ski mask) for the mouth
one playing period (from tee to green) on a golf course
informal terms for the mouth
an opening into or through something
a depression hollowed out of solid matter
an unoccupied space
informal terms for a difficult situation
a fault

hole (verb)	mouth hole (verb)
make holes in
hit the ball into the hole